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Yens improvement to Bellman-Ford Suppose that we order the

ISBN: 9780262033848 130

Solution for problem 24-1 Chapter 24

Introduction to Algorithms | 3rd Edition

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Introduction to Algorithms | 3rd Edition

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Problem 24-1

Yens improvement to Bellman-Ford Suppose that we order the edge relaxations in each pass of the Bellman-Ford algorithm as follows. Before the first pass, we assign an arbitrary linear order 1; 2;:::;jV j to the vertices of the input graph G D .V; E/. Then, we partition the edge set E into Ef [ Eb, where Ef D f.i; j / 2 E W ij g. (Assume that G contains no self-loops, so that every edge is in either Ef or Eb.) Define Gf D .V; Ef / and Gb D .V; Eb/. a. Prove that Gf is acyclic with topological sort h1; 2;:::;jV ji and that Gb is acyclic with topological sort hjV j; jV j1;:::;1i. Suppose that we implement each pass of the Bellman-Ford algorithm in the following way. We visit each vertex in the order 1; 2;:::;jV j, relaxing edges of Ef that leave the vertex. We then visit each vertex in the order jV j; jV j1;:::;1, relaxing edges of Eb that leave the vertex. b. Prove that with this scheme, if G contains no negative-weight cycles that are reachable from the source vertex s, then after only djV j =2e passes over the edges, :d D .s; / for all vertices 2 V . c. Does this scheme improve the asymptotic running time of the Bellman-Ford algorithm?

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2/29/2016  Cognitive Task Analysis o Methods for decomposing job & task performance into discrete, measurable units with special emphasis on eliciting mental processes & knowledge content o Think-aloud protocol  Approach that investigates thought processes of experts who achieve high levels of performance o Time consuming & requires a good deal of expertise to do well o Consider the following to determine whether cognitive task analysis may be worthwhile:  Persistent performance problems  Costly errors or accidents  Training difficult to transfer to job behavior  Takes a long time to achieve high levels of performance  New Addition of Job Analysis Instruments o Personality-Related Position Requirements Form (PPRF)  Devoted to identifying personality predictors of job performance  Intended to supplement job analysis  Summary of Job Analysis Process o The more information gathered from the greatest number of sources, the better the job analyst can understand the job o Most job analyses should include considerations of personality demands & work context  Occupational Information Network of O*NET o Introduced by federal government to replace the Dictionary of Occupational Titles (D.O.T.) o Electronic medium, so it can be updated instantaneously as changes occur  Competency Modeling o Identifies characteristics desired across all individuals & jobs within an organization o Connects individuals with organizational viability & profitability o Natural extension of job analysis logic, rather than a replacement  Job Evaluation, Comparable Worth, & the Law o Job evaluation: Method for making internal pay decisions by comparing job titles to one another & determining their relative merit o Compensable factors o Skills, responsibility, effort, & working conditions o Equal Pay Act of 1963: requires “equal pay for equal work.”  Comparable Worth o Notion that people who are performing jobs of comparable worth to an organization should receive comparable pay o In the end, comparable worth is concerned with the social value of fairness  Job Analysis & Employment Litigation o Competent job analysis does not guarantee validity, but absence of credible job analysis could be very damaging o Growing gap between evolution of I-O psychology & Uniform Guidelines on Employee Selection Procedures (1978) o SIOP Principles (2003) are more updated and consistent with current research Chapter 5—Performance Measurement  Basic Concepts in Performance Measurement o Uses for performance information  Criterion data  Employee development  Motivation/satisfaction  Rewards  Promotion  Layoff  Types of Performance Data o Objective o Personnel o Judgmental  Performance Measurement o Relationships among performance measures o Hands-on performance measures  Employee engages in work-related tasks  Include carefully constructed simulations  Walk-through testing  Employee describes in detail how to do a job o Electronic performance monitoring  Commercial Driving Fleets  Improving Performance  Computer Usage at Work  Worker Attitudes  What steps should employers take to improve attitudes  Performance Management o Emphasizes link between individual behavior & organizational strategies & goals o 3 Components of Performance Management  Definition of performance  Actual measurement process  Communication between supervisor & subordinate about individual behavior & organ. expectations  Perceptions of Fairness in Performance Measurement o Factors associated with fairness measurement  Appraisal frequency positively related to fairness perceptions  Joint planning with supervisor to eliminate weaknesses enhances fairness perception  Supervisor’s knowledge of duties of person being measured  Supervisor’s knowledge of actual performance of person being rated o Distributive justice  Fairness of outcomes related to decisions  You get something as a result of your behavior; i.e. promotion, bonus, fired o Procedural justice  Fairness of process by which ratings are assigned & a decision is made  Is the process fair o Interpersonal justice  Respectfulness & personal tone of communications surrounding evaluation 3/2/2016  Performance Rating—Substance o Theories of performance rating  Process model—who rates who  Addresses various factors comprising rating process  Content model—what is being rated and how it is rated  Addresses content input to supervisory ratings  Rating context—why is it being rated  Includes both announced purpose & other, non- announced agendas surrounding ratings  Need to be aware of the different reasons authorities have  Focus on Performance Ratings o Overall performance ratings  Provide a number to describe how you perform different tasks in relation to contextual performance and counter- productive performance; this helps compare two people  Influenced by 3 factors  Task performance  Contextual performance/OCB  Counter-productive performance  Performance Ratings o Trait ratings – a warning; rates aspects of personality  E.g. I am aloof, abrasive  Can’t be fired just off of trait ratings; can’t change personality o Task-based ratings  Effectiveness of employee in accomplishing duties  Most easily defended in court; can be fired because of this o Critical incidents method  Examples of critical behaviors that influence performance  i.e. how one goes about getting robbed in the bank; behaviors o Structural characteristics of performance rating scale  Extent to which duty/characteristic being rated is behaviorally defined (should not be defined by personality!!)  Extent to which meaning of response categories is defined  Degree that person interpreting ratings can understand response that rater intended  Rating Formats o Graphic rating scales (most common)  Graphically display performance scores running from high to low o Checklist  List of behaviors presented to rater who places a check next to items that best (or least) describe the ratee o Weighted checklist  Included items have assigned values or weights; can have fractured ratings o Forced-Choice Format  Requires the rater to choose two statements out of four that could describe the ratee o Behaviorally anchored rating scales (BARS)  Rating format that includes behavioral anchors describing what worker has done, or might be expected to do, in a particular duty area 3/4/2016  Employee Comparison Methods o Involve direct comparison of 1 person w/another o Simple ranking  Employees ranked from top to bottom according to assessed proficiency o Paired comparison  Each employee in a group is compared with each other individual in the group o Useful in making layoff or downsizing decisions o Feedback is difficult because there is no clear standard of performance o Difficulty in comparing individuals in different groups  Performance Rating—Process o Rating sources  Supervisors  Most common information source  Many actively avoid evaluation & feedback  Peers  More likely to know about a worker’s typical performance  Conflict of interest likely when competing for fixed resources  Self-Ratings o Discussion of ratings with supervisor increases perceptions of procedural fairness o Potential for distortion & inaccuracy  Minimized with supervisor discussion o Conflict of interest if used for administrative purposes  Rating Sources o Subordinate ratings  Critical that subordinate feedback be kept anonymous o Customer & supplier ratings  Important from business strategy vantage point o 360 degree systems  Collect & provide an employee with feedback that comes from many sources  Often used for feedback & employee development  Rating Distortions o Central tendency error  Raters choose mid-point on scale to describe performance when more extreme point is more appropriate o Leniency-severity error  Raters are unusually easy or harsh in their ratings o Halo error  Same rating is assigned to an individual on a series of dimensions, causing the ratings all to be similar; lack of identification of strengths and weaknesses  A “halo” surrounds the ratings  Rater Training o Some distortions (errors) may be corrected through training o Administrative training  Important for uncommon rating systems (e.g., BARS) or if 1 or more structural characteristics are deficient o Psychometric training  Makes raters aware of common rating errors in hopes of reducing such errors  Framer of Reference Training o Based on assumption that rater needs context for providing rating  Basic steps  Provide information about multidimensional nature of performance  Ensure raters understand meaning of scale anchors  Engage in practice rating exercises of standard performance  Provide feedback on practice exercise  Reliability & Validity of Performance Rating o Reliability  Currently the subject of lively debate  Inter-rater reliability considered poor but this isn’t necessarily bad considering each rater relies on a different perspective o Validity  Depends on manner by which rating scales were conceived & developed

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ISBN: 9780262033848

The answer to “Yens improvement to Bellman-Ford Suppose that we order the edge relaxations in each pass of the Bellman-Ford algorithm as follows. Before the first pass, we assign an arbitrary linear order 1; 2;:::;jV j to the vertices of the input graph G D .V; E/. Then, we partition the edge set E into Ef [ Eb, where Ef D f.i; j / 2 E W ij g. (Assume that G contains no self-loops, so that every edge is in either Ef or Eb.) Define Gf D .V; Ef / and Gb D .V; Eb/. a. Prove that Gf is acyclic with topological sort h1; 2;:::;jV ji and that Gb is acyclic with topological sort hjV j; jV j1;:::;1i. Suppose that we implement each pass of the Bellman-Ford algorithm in the following way. We visit each vertex in the order 1; 2;:::;jV j, relaxing edges of Ef that leave the vertex. We then visit each vertex in the order jV j; jV j1;:::;1, relaxing edges of Eb that leave the vertex. b. Prove that with this scheme, if G contains no negative-weight cycles that are reachable from the source vertex s, then after only djV j =2e passes over the edges, :d D .s; / for all vertices 2 V . c. Does this scheme improve the asymptotic running time of the Bellman-Ford algorithm?” is broken down into a number of easy to follow steps, and 222 words. Introduction to Algorithms was written by and is associated to the ISBN: 9780262033848. This full solution covers the following key subjects: vertex, ford, order, bellman, Pass. This expansive textbook survival guide covers 35 chapters, and 151 solutions. This textbook survival guide was created for the textbook: Introduction to Algorithms, edition: 3. The full step-by-step solution to problem: 24-1 from chapter: 24 was answered by , our top Engineering and Tech solution expert on 11/10/17, 05:55PM. Since the solution to 24-1 from 24 chapter was answered, more than 610 students have viewed the full step-by-step answer.

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Yens improvement to Bellman-Ford Suppose that we order the